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2) Is there any need to put a base of sand in the trench or just lay the pipe on the dirt? (gravelly/small rocks)
Need? No... but it's better practise. Gravel tends to settle more over time than equally compacted sand. 'Tis more likely to form cavities under the pipework, removing support and leading to low points that'll collect sediments which can cause blockages or, in worst cases, breakages. The bedding sand doesn't need to be deep, you can get away with only an inch or so if the trench was dug competently and had appropriate fall.